Wigner-Yanase Spectrum Ordering

Abstract

The five members of the Wigner-Yanase contraction spectrum are strictly increasing.

Theorem 1.1 (The five-member Wigner-Yanase spectrum is strictly ordered).

$$1<\frac{1}{2(1-\log 2)}<2<\frac{6}{11-12\log 2}<\frac{1}{1-\log 2}$$

Proof. Machine-checked in Lean as D5/S3/Constants/WignerYanaseSpectrum.wy_contraction_spectrum_strict_order (✓ std3). ∎

Source. Repository-derived.

Commentary.

The Wigner-Yanase contraction spectrum reported for the divergence tower consists of the five values 1, 1/(2(1 - ln 2)), 2, 6/(11 - 12 ln 2), and 1/(1 - ln 2), where ln 2 denotes the natural logarithm of two. Using the elementary bounds 0.6931471803 < ln 2 < 0.6931471808 (so that 1 - ln 2 > 0 and 11 - 12 ln 2 > 0), each successive strict inequality reduces to a linear bound on ln 2 and is discharged by clearing the positive denominators.

The theorem establishes only this strict ordering of the reported spectrum values; it does not derive why these are the Wigner-Yanase contraction coefficients, nor does it cover the J-relations or the partner-anonymity clause of the note.

References

• Truth anchor: D5/S3/Constants/WignerYanaseSpectrum.wy_contraction_spectrum_strict_order